SUMMARY

Foraging desert ants return to their starting point, the nest, by means of
path integration. If the path-integration vector has been run off but the nest
has not yet been reached, the ants engage in systematic search behavior. This
behavior results in a system of search loops of ever increasing size and
finally leads to a search density profile peaking at the location where the
path integration system has been reset to zero. In this study we investigate
whether this systematic search behavior is adapted to the uncertainty
resulting from the preceding foraging run. We show first that the longer the
distances of the foraging excursions, the larger the errors occurring during
path integration, and second that the ants adapt their systematic search
strategy to their increasing uncertainty by extending their search pattern.
Hence, the density of the systematic search pattern is correlated with the
ants' confidence in their path integrator. This confidence decreases with
increasing foraging distances.

Introduction

Foraging desert ants, Cataglyphis fortis, return to their nest by
keeping a running total of their distance and direction from the nest. This
mode of navigation was called path integration by Mittelstaedt and
Mittelstaedt (Mittelstaedt and
Mittelstaedt, 1982), who provided the first systematic studies of
this phenomenon, and vector navigation by Wehner
(Wehner, 1982;
Wehner, 1983). More recent
reviews and considerations on path integration are given elsewhere
(Wehner and Srinivasan, 2003;
Merkle et al., 2006). By path
integration the ants acquire a home vector that enables them to return at any
time along the beeline, so to speak, to the nest. However, after having played
out their home vector, they do not always arrive exactly at the entrance of
their nest, a tiny hole in the desert floor. Even small deviations or
inaccuracies within the compass, the odometer or the integration system lead
to overall errors that might result in remarkable discrepancies between the
tip of the home vector, i.e. the nest position as computed by the ant's path
integrator, and the actual position of the nest. This should lead to an
increasing uncertainty about the goal with increasing foraging distances. That
such an uncertainty can cause a change in behavior has already been shown
(Wolf and Wehner, 2005). Wolf
and Wehner demonstrated that desert ants when leaving the nest deviate from
the direct global vector course with the direction of the blowing wind, and
then head towards a food source against the direction of the wind, i.e. they
approach the feeder in a way that enables them to head straight upwind towards
the feeder by following the odor plume emanating from it. The upwind approach
distance depends on the length of the foraging trip. The authors interpret
this behavior as being an error compensation strategy due to navigation
uncertainty, and regard it as one tool that outbound ants apply to deal with
the errors they perform during path integration. Here we aimed to test ants on
their way back from the feeder to the nest, i.e. inbound ants, and tried to
quantify the correlation between uncertainty about the path integrator and the
length of the foraging runs.

If an ant fails to find the nest after having `run off' its home vector, it
terminates its almost straight inbound run and starts a systematic search for
the nest (Wehner and Srinivasan,
1981). During this search C. fortis performs loops of
increasing radius around the supposed nest position
(Wehner and Wehner, 1986). At
regular intervals, it reverts to the starting point of the systematic search,
i.e. the nest position as calculated by the path integrator, and then changes
the direction in which it heads off next. Desert ants as well as desert
isopods (Hemilepistus reaumuri) spatially broaden their search the
farther they have ventured out during their foraging trips
(Hoffmann, 1983a) [fig. 3.35 in
(Wehner, 1992)].

The ultimate reason for this change of the search pattern with increasing
distance of their foraging journeys could be an ongoing accumulation of errors
during the egocentric path integration process. We designed and applied an
experimental paradigm, which allowed us to compare the orientation errors
resulting from different homing distances with the spatial layout of the
subsequent search. By this we investigated whether the search density profile
is adapted to the degree of uncertainty inherent in the path integration
process. In particular, our experiment was intended to reveal (i) whether
different lengths of the foraging paths account for differences in the errors
produced by the path integrator, and, if this were the case, (ii) whether
Cataglyphis ants adjust their systematic search behavior
accordingly.

Experimental paradigm. (A) Training situation. Ants trained to a feeder
located either 5 m, 10 m or 20 m south of the nest entrance were captured at
the feeder and transferred to the test field. Filled square, nest; open
square, feeder where the ants later were captured and transferred to the test
field. (B) Example of a trajectory of an ant transferred from the feeder to
the test field. Open circle: point of release; filled circle: correct position
of the (fictive) nest; open triangle: end of home vector; filled triangle:
center of systematic search (for definition of end of home vector and center
of systematic search see data analysis); mesh width of grid was 1 m.

If this again were the case, the search pattern would reflect the ant's
degree of confidence in the output of its path integrator.

Materials and methods

The experiments were performed within a salt-pan near Maharès,
southern Tunisia (34.58°N, 10.50°E) from June to September 2004. All
ants belonged to the same colony, which had not changed its nest location over
at least 5 years (Dillier and Wehner,
2004).

Training procedure

Desert ants Cataglyphis fortis (Forel 1902,
Wehner 1983) were trained to
feeders south of their nest (Fig.
1A). The distances between nest and feeder were varied
systematically (5 m, 10 m, 20 m, Fig.
1A). All ants were marked at the feeder at least 1 day prior to
the tests in order to ensure that the ants used in the experiments had
performed a sufficient number of foraging trips before they were tested
(Åkesson and Wehner,
2002). There were no obvious landmarks within the range of vision
of the foraging ants on their outbound and inbound runs as well as around the
nest and the feeder. Thus, the ants had to rely upon their celestial compass
information exclusively, i.e. they had no landmarks to reduce possible errors
that had accumulated during path integration.

Test procedure

Our experiment aimed at testing whether the foraging distance affects the
errors accumulating during foraging as well as the range of the subsequent
search pattern. Ants that were trained to a feeder 5 m (in the following
called 5-m ants, N=51), 10 m (10-m ants, N=53), or 20 m
(20-m ants, N=50) south of the nest were captured at the feeder,
transferred in small black plastic flasks to the test area, and released there
with a piece of biscuit or a dead fly in their mandibles. The test area was
about 100 m apart from the training area. A sandy bank separated the nest and
the test area. Thus, it was very unlikely that the ants had ever been in the
test area before. Like the training area the test area did not contain any
obvious landmarks. The paths of the ants were recorded by means of a white
grid (20×30 m) that had been painted on the flat ground [for recording
paradigms, see (Wehner,
1982)].

The ants ran off their home vectors, and then switched on their systematic
search program. The trajectories of all ants were recorded for 5 min on graph
paper. Only for the 20-m ants, were the trajectories recorded for 10 min each,
because of the larger loops and the longer home runs of these ants.

Data analysis

The recorded trajectories were digitized using a graphics tablet and GEDIT
Graphics Editor and Run Analyser (Antonsen,
1995). For all animals that still had to run off the home vector,
home vectors and systematic searches were digitized separately. The switch
from playing out the home vector to systematic search behavior was defined as
the point at which the overall direction of the path changed by at least
30°. An additional condition was that the animal did not revert to the
former general direction for the next 3 m. In most cases, one could discover
this point easily as a sharp turn performed by the animal
(Fig. 1B).

To test whether the three different groups of ants captured at the nest
(5-m ants, 10-m ants, 20-m ants) varied with regard to the accuracy of their
home vectors, we determined for each ant the distance between the end of each
home vector and the fictive position of the nest
(Fig. 1B). In addition, we
calculated the distance between the center of the systematic search and the
correct position of the nest. The center of the systematic search was defined
as the square (0.5 m×0.5 m) that contained the highest path density,
i.e. in which the ant's path length divided by the total path length of the
systematic search of this particular ant reached its maximum
(Fig. 1B). If the density in
two squares was the same, the respective ant was excluded from the systematic
search analysis. This was the case in only about 10% of all cases
(N=154). Thus, the error performed during path integration was
measured for both the home run (distance between end of straight home run and
correct position of nest) and the subsequent systematic search (distance
between center of search and correct position of nest).

End points of home runs (circles) and systematic search centers (stars) of
(A) 5-m, (B) 10-m, and (C) 20-m ants. The trajectories were recorded for five
respective 10 min searches (see Materials and methods). The correct position
of the nest was at the intersection of 0/0.

In order to compare the systematic search patterns among all ants, we have
cut the systematic search runs at a path length of 40 m, i.e. each ant had
completed at least two search loops. Animals with systematic search runs
shorter than this criterion were excluded from this analysis (16% of all runs,
N=154). The distances between the most extreme values along both the
x and the y axes were than multiplied by each other. This
resulted in an area characterizing the spatial extension of the systematic
search.

Statistics

Multiple comparisons between the groups were done using the Kruskal-Wallis
one-way analysis of variance (ANOVA). Tests between single groups were
performed using Dunn's post-hoc test.

Results

Since we do not know the exact position at which an ant suspects its nest
to be, we used two different parameters to measure the accuracy of the ant's
path integration system. Various procedures have been applied to determine the
`end point' of an ant's home run, i.e. the point at which the ant assumes its
nest to be (e.g. Wehner and Srinivasan,
1981; Collett et al.,
1998; Bisch-Knaden and Wehner,
2003). However, one cannot be sure whether this point really
reflects the ant's guess of its nest position, or whether at this point the
ant has already started its first search loop. As an ant should focus its
search at that position, at which it assumes its nest to be, the position of
the ant's search density peak might yield clearer results about the ant's
perspective of the position of the nest.
Fig. 2 correlates the ends of
the home runs determined as described in the Materials and methods section,
and the centers of the systematic search with the correct position of the nest
for all three groups. By using these data sets we compared the distance
between the end of each home run and its corresponding center of search with
the average distance to the centers of search by all ants. As a result, the
end of the home run of a particular ant is closer to the center of systematic
search of this particular ant (5-m ants: median=2.08 m, N=49; 10-m
ants: median=3.12 m, N=41; 20-m ants: median=3.78 m, N=49)
than to the centers of systematic search of all other ants (5-m ants:
median=2.24 m, N=49, Wilcoxon matched-pairs signed-ranks test:
P=0.395; 10-m ants: median=3.76, N=41, P<0.05;
20-m ants: median=5.05 m, N=49, P<0.01). Therefore, we
can conclude that for each individual ant there is indeed a correlation
between the end of the home run and the center of systematic search.
Nevertheless, since the median distance between the end of the home run as
determined by the experimenter and the center of the ant's search is rather
large, for further analyses we decided to take both parameters into account
(Fig. 3).

The main focus of the present account was to test whether the ant's
accuracy in pointing at the nest position is affected by the length of the
preceding foraging trip. The accuracy was reduced after longer foraging trips.
Ants that returned from a feeder 10 m and 20 m away from the nest started
their systematic search behavior farther away from the fictive nest position
than ants that returned from a distance of only 5 m
(Fig. 3A). Furthermore, the
distance between the center of the systematic search and the correct position
of the nest increased with increasing foraging distance
(Fig. 3B).

Accuracy of the path integrator. (A) Distances between the end of the home
run and the correct position of the nest for ants captured at the feeder (5-m
ants: median=1.27 m, N=51; 10-m ants: median=2.45 m, N=53;
20-m ants: median=2.47 m, N=50). Boxplots give the median, 25% and
75% quartiles, whiskers and outliers (+). (B) Distances between the center of
the systematic search and the correct position of the nest for ants captured
at the feeder (5-m ants: median=2.00 m, N=49, 10-m ants: median=3.04
m, N=41, 20-m ants: median=4.30 m, N=49). The values for the
Kruskal-Wallis (KW) one-way ANOVA are given at the top, the P values
of pairwise comparison are given underneath. P values that show
significant differences at a level of at least 5% are printed in bold
types.

Is this increasing error also reflected in the ants' confidence in their
path integrator? In trying to answer this question, we compared the range of
the systematic search patterns of the three different groups. Again, the ants
that had returned from a distance of only 5 m differed dramatically from those
that had foraged over longer distances
(Fig. 4). Hence, the ants seem
to be aware of the correlation that obviously exists between the errors
accumulated during path integration and the foraging distance
(Fig. 3), and respond
accordingly by broadening their search pattern with increasing foraging
distance (Fig. 4).

Discussion

Do different lengths of foraging runs cause larger errors of the path
integrator?

We tested whether longer distances of foraging trips account for larger
errors in the path integrator. Both the accuracy of the home vector and the
systematic search behavior were more accurate for ants heading back after
shorter foraging excursions (Fig.
3). Therefore, longer distances do lead to a decreasing accuracy
of the path integrator. This increase of the path integration error with the
covered distance leads us to the next question: Is this increasing error also
reflected in the ants' confidence in their path integrator?

Several models describe the search behavior of desert arthropods as
mathematical functions (Wehner and
Srinivasan, 1981; Hoffmann,
1983a; Hoffmann,
1983b; Alt, 1995).
The systematic search program of desert ants is not an equidistant spiral, but
rather concentrated around the area in which the nest is most likely to be
found (Müller and Wehner,
1994). Hence, the search density profile gets adapted to the
probability density function of the target. Now, does the search pattern also
get adapted to path integration errors, which, as shown above, increase with
larger foraging distances? Cataglyphis indeed adapts its search
behavior to the larger errors by widening its search loops
(Fig. 4). Obviously, its
confidence in its path integrator seems to be lower, the larger the foraging
distance it has covered before finding a food item. Ecologically speaking, it
is essential for the ants to reach the nest in the shortest possible time. If
the errors to be expected are small, the ants should concentrate their
searches around the end of the home vector, and this is exactly what they do.
On the other hand, the bigger the uncertainty of the ants gets, the wider the
spread of the loops, and again this is what we observed.

Uncertainty is an inherent property of the odometer, the compass and the
path integrator and, therefore, surely cannot be measured by the ants. Thus,
it seems to be a successful strategy to take the uncertainty into account by
widening the systematic search after longer foraging excursions as shown in
our experiment. However, it might well be that in the very same training
situation an ant behaves as if it decreased the size of its uncertainty range
[e.g. during an upwind approach to the feeder (see
Wolf and Wehner, 2000)]. Other
experiments, in contrast, have shown that during continuous training the ants
are not able to increase the accuracy of their outbound or inbound runs (T.M.
and R.W., unpublished).

To sum up, our results provide clear evidence that the ant's systematic
search behavior is not a fixed program that is just reeled off after the
animal has completed its home vector. Rather, the search program is highly
adaptive and enables the ants to take errors into account that necessarily
accumulated during path integration.

ACKNOWLEDGEMENTS

This study was supported by the Swiss National Science Foundation (grant
no. 3100-61844, to R.W.) and the Research Group Wissensformate of
Bonn University. T.M. would like to thank M. Rost for help with the data
analysis.

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